PSA_LEVEL-UP_QNR7. Consider the function f(x) = max (7-x, x+3). In which range does f take its minimum value?
A) -6 ≤ x ≤-2
B) -2 ≤ x < 2
C) 2 ≤ x ≤ 6
A) 6 ≤ x ≤ 10
To get a rough sketch of f(x), let us first draw the lines y= 7-x and y = x+3.
We see the lines intersecting at a certain point. Now to find out max(7-x, x+3), we need to understand that for all the values of x we need to find out the maximum out of 7-x and x-3 and this can be shown as the below graph. [Dotted lines are excluded as we need to take maximum out of the two lines; in short, for all the values of x that lie to the left of the intersection point max is 7-x whereas for all the values to the right, the max is given by line x-3].
Now, it is clear from the above that minimum value of f(x) is nothing but the intersection point which can be found by equating both the line equations:
=> x= 2. Option C satisfies this.